Note that the limit (REF ) need not exist, however, one may ask the same questions for the upper and lower limits, defined by replacing the limit by \(\limsup \)  and \(\liminf \)  respectively. Even for the simplest families of number fields, i.e. imaginary/real quadratic fields, such questions have proved difficult. On the other hand, the systematic study of arithmetic statistics for the Iwasawa invariants of elliptic curves was initiated by the second named author, and has gained considerable momentum in the following works: [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}.
